When you choose automatic weights does it have settings?
For more control you could use the Envelope Weights instead. For this, select your armature and set its Display properties to 'Envelope'. The bones will now show in 'Edit mode' surrounded with a halo indicating the extent of the envelope and this can be varied for each bone via the properties panel ('N') via the Envelope attribute. The reach of influence of that bone is also affected by the Head and Tail radius. When the armature is parented to a mesh via the 'With Envelope Weights' option, the reach of the envelope will affect the influence of each bone.